To rotate tubing within a well, drilling rigs often have top drives that are suspended from drilling masts. When the top drives rotate the tubing, torque generated by the top drives must be transmitted to the rear of the mast and into the supporting structure. For this purpose, it is conventional to provide a torque carrier running along the height of the mast along which the top drive slides. The torque carrier is fastened to the mast to transmit torque into the mast. Larger rigs also are equipped with upper and lower masts that can be telescoped together for transport. When these larger telescoping rigs are dismantled, the torque carrier must be removed to allow the upper mast to telescope into the lower mast. This process is time consuming. This invention is directed to a telescoping rig with torque carrier that facilitates readying a rig for transport.